Afficher O et O'

Afficher le patron

Paramètres de la perspective

Paramètres du parallélépipède rectangle

Selon u

Selon v

Selon w

Ouvert

Fermé

Patron ouvert
vu du dessus

O_3: {0, 0, 0}
i_3: {1, 0, 0}
j_3: {0, 1, 0}
k_3: {0, 0, 1}
θ = 0.6632251157578453 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
φ = 0.5061454830783556 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
P: {-sin(θ), cos(θ), 0, -cos(θ) sin(φ), -sin(θ) sin(φ), cos(φ), cos(θ) cos(φ), sin(θ) cos(φ), sin(φ)}
P': {-sin(θ), cos(θ), 0, -cos(θ), -sin(θ), 0, 0, 0, 1}
O_0: (Element[O_3, 1], Element[O_3, 2])
i = Vector(O_0, (Element[i_3, 1], Element[i_3, 2]))
j = Vector(O_0, (Element[j_3, 1], Element[j_3, 2]))
u = Vector(O_0, (Element[P, 1] Element[i_3, 1] + Element[P, 2] Element[i_3, 2] + Element[P, 3] Element[i_3, 3], Element[P, 4] Element[i_3, 1] + Element[P, 5] Element[i_3, 2] + Element[P, 6] Element[i_3, 3]))
v = Vector(O_0, (Element[P, 1] Element[j_3, 1] + Element[P, 2] Element[j_3, 2] + Element[P, 3] Element[j_3, 3], Element[P, 4] Element[j_3, 1] + Element[P, 5] Element[j_3, 2] + Element[P, 6] Element[j_3, 3]))
w = Vector(O_0, (Element[P, 1] Element[k_3, 1] + Element[P, 2] Element[k_3, 2] + Element[P, 3] Element[j_3, 3], Element[P, 4] Element[k_3, 1] + Element[P, 5] Element[k_3, 2] + Element[P, 6] Element[k_3, 3]))
coefEq: {1, 0, 1 / sin(φ)^(2)}
Eq: Element[coefEq, 1] x^(2) + Element[coefEq, 2] x y + Element[coefEq, 3] y^(2) = 1
coefMer_0: {(Element[P, 6]^(2) + Element[P, 4]^(2)) / (Element[P, 1] Element[P, 6] - Element[P, 4] Element[P, 3])^(2), -2 * (Element[P, 3] Element[P, 6] + Element[P, 4] Element[P, 1]) / (Element[P, 1] Element[P, 6] - Element[P, 4] Element[P, 3])^(2), (Element[P, 3]^(2) + Element[P, 1]^(2)) / (Element[P, 1] Element[P, 6] - Element[P, 4] Element[P, 3])^(2)}
Mer_0: Element[coefMer_0, 1] x^(2) + Element[coefMer_0, 2] x y + Element[coefMer_0, 3] y^(2) = 1
coefMer_{90}: {(Element[P, 6]^(2) + Element[P, 5]^(2)) / (Element[P, 2] Element[P, 6] - Element[P, 5] Element[P, 3])^(2), -2 * (Element[P, 3] Element[P, 6] + Element[P, 5] Element[P, 2]) / (Element[P, 2] Element[P, 6] - Element[P, 5] Element[P, 3])^(2), (Element[P, 3]^(2) + Element[P, 2]^(2)) / (Element[P, 2] Element[P, 6] - Element[P, 5] Element[P, 3])^(2)}
Mer_{90}: Element[coefMer_{90}, 1] x^(2) + Element[coefMer_{90}, 2] x y + Element[coefMer_{90}, 3] y^(2) = 1
horiz_1 = Translate(xAxis, Vector[19 / 2 j])
horiz_2 = Translate(xAxis, Vector[17 / 2 j])
horiz_3 = Translate(xAxis, Vector[15 / 2 j])
horiz_4 = Translate(xAxis, Vector[13 / 2 j])
horiz_5 = Translate(xAxis, Vector[11 / 2 j])
horiz_6 = Translate(xAxis, Vector[9 / 2 j])
horiz_7 = Translate(xAxis, Vector[7 / 2 j])
horiz_8 = Translate(xAxis, Vector[5 / 2 j])
vert_1 = Translate(yAxis, Vector[-9 / 2 i])
vert_2 = Translate(yAxis, Vector[-1 / 2 i])
L_1 = 2 (slider from 1 to 10, step 0.5)
L_2 = 3 (slider from 1 to 10, step 0.5)
L_3 = 3 (slider from 1 to 10, step 0.5)
Ψ = 0.22689280275926285 rad (slider from 0 to 1.5707963267948966, step 0.017453292519943295)
M_1: (Element[P, 1] cos(Ψ) + Element[P, 3] sin(Ψ), Element[P, 4] cos(Ψ) + Element[P, 6] sin(Ψ))
M_2: (Element[P, 2] cos(Ψ) + Element[P, 3] sin(Ψ), Element[P, 5] cos(Ψ) + Element[P, 6] sin(Ψ))
M_3: (-Element[P, 1] cos(Ψ) + Element[P, 3] sin(Ψ), -Element[P, 4] cos(Ψ) + Element[P, 6] sin(Ψ))
M_4: (-Element[P, 2] cos(Ψ) + Element[P, 3] sin(Ψ), -Element[P, 5] cos(Ψ) + Element[P, 6] sin(Ψ))
Mer_{M2} = Translate(Mer_{90}, Vector[Vector[O_0, M_2]])
M_5: (Element[P, 2] cos(2 Ψ) + Element[P, 3] sin(2 Ψ), Element[P, 5] cos(2 Ψ) + Element[P, 6] sin(2 Ψ)) + Vector[O_0, M_2]
AffO = true
O = (9, 6)
A_1: O + L_1 / 2 u - L_2 / 2 v
A_2: O + L_1 / 2 u + L_2 / 2 v
A_3: O - L_1 / 2 u + L_2 / 2 v
A_4: O - L_1 / 2 u - L_2 / 2 v
Base_b, a_1, a_2, a_3, a_4 = Polygon(A_1, A_2, A_3, A_4)
B_1: A_1 + L_3 Vector[O_0, M_1]
B_2: A_2 + L_3 Vector[O_0, M_1]
Lat_1, a_5, a_6, b_2, b_1 = Polygon(A_1, A_2, B_2, B_1)
B_3: A_2 + L_3 Vector[O_0, M_2]
B_4: A_3 + L_3 Vector[O_0, M_2]
Lat_2, a_7, a_8, b_4, b_3 = Polygon(A_2, A_3, B_4, B_3)
B_5: A_3 + L_3 Vector[O_0, M_3]
B_6: A_4 + L_3 Vector[O_0, M_3]
Lat_3, a_9, a_{10}, b_6, b_5 = Polygon(A_3, A_4, B_6, B_5)
B_7: A_4 + L_3 Vector[O_0, M_4]
B_8: A_1 + L_3 Vector[O_0, M_4]
Lat_4, a_{11}, a_{12}, b_8, b_7 = Polygon(A_4, A_1, B_8, B_7)
C_1: B_3 + L_2 Vector[M_2, M_5]
C_2: B_4 + L_2 Vector[M_2, M_5]
Base_h, b_9, b_{10}, c_2, c_1 = Polygon(B_3, B_4, C_2, C_1)
u' = Vector(O_0, (Element[P', 1] Element[i_3, 1] + Element[P', 2] Element[i_3, 2] + Element[P', 3] Element[i_3, 3], Element[P', 4] Element[i_3, 1] + Element[P', 5] Element[i_3, 2] + Element[P', 6] Element[i_3, 3]))
v' = Vector(O_0, (Element[P', 1] Element[j_3, 1] + Element[P', 2] Element[j_3, 2] + Element[P', 3] Element[j_3, 3], Element[P', 4] Element[j_3, 1] + Element[P', 5] Element[j_3, 2] + Element[P', 6] Element[j_3, 3]))
AffPat = true
O' = (9.58, 0)
A'_1: O' + L_1 / 2 u' - L_2 / 2 v'
A'_2: O' + L_1 / 2 u' + L_2 / 2 v'
A'_3: O' - L_1 / 2 u' + L_2 / 2 v'
A'_4: O' - L_1 / 2 u' - L_2 / 2 v'
Base'_b, a'_1, a'_2, a'_3, a'_4 = Polygon(A'_1, A'_2, A'_3, A'_4)
B'_1: A'_1 + L_3 u'
B'_2: A'_2 + L_3 u'
Lat'_1, a'_5, a'_6, b'_2, b'_1 = Polygon(A'_1, A'_2, B'_2, B'_1)
B'_3: A'_2 + L_3 v'
B'_4: A'_3 + L_3 v'
Lat'_2, a'_7, a'_8, b'_4, b'_3 = Polygon(A'_2, A'_3, B'_4, B'_3)
B'_5: A'_3 - L_3 u'
B'_6: A'_4 - L_3 u'
Lat'_3, a'_9, a'_{10}, b'_6, b'_5 = Polygon(A'_3, A'_4, B'_6, B'_5)
B'_7: A'_4 - L_3 v'
B'_8: A'_1 - L_3 v'
Lat'_4, a'_{11}, a'_{12}, b'_8, b'_7 = Polygon(A'_4, A'_1, B'_8, B'_7)
C'_1: B'_3 + L_2 v'
C'_2: B'_4 + L_2 v'
Base'_h, b'_9, b'_{10}, c'_2, c'_1 = Polygon(B'_3, B'_4, C'_2, C'_1)
T': A'_1 + 2 u' - 2 v'